Apparently Russia has only sent in 30% of their troops into Ukraine, so to have got as far as they have in that period of time is quite impressive.
It's almost impossible for them to overrun Keiv, as it's too big and too heavy defended. Russia isn't just bombing the fuck out of the city that would have happened in WW2, so to make your way into the city street by street will be hard fought and cost many lives. I think Russia has three objectives.
1. Take out the government. Try to find the President and kill him along with his cabinet.
2. Encircle Kiev, cut it off from supplies such as water, food and such and wait it out until a surrender happens.
3. Take over certain areas of Ukraine such as Dombass, Odessa etc to reduce the size of Ukraine and the threat they pose by destroying all military infrastructure.
They appear to be trying to limit civilian deaths, and all the interactions I have seen between them an angry locals they seem to be quite well manured, maybe even embarrassed by being there.